## PCA

Normalized data matrix: $X_{N \times D}$, where N is number of data and D is dimension of data.
$S=\frac{1}{N}(X^T X)_{D \times D}$ is the covariance matrix. $S_{ij}=\frac{1}{N}\sum\limits_{k=1}^n X_{ki} X_{kj}$ .


